Does having a master's degree increase your ability to be hired?
Yes! I live in Sweden and have recruited people every now and then over a long period of time.
Key things I look for in new hires are:
1) Personal impression - would you fit into our workplace?
2) Energy, drive, where are you going? What is your key interests... does it match what we are looking for?
3) Proof points of consistent performance -- strong references help but not relevant if it is your first job. Here a completed degree is very valuable. Stating that "I took the classes and learned all I need but didn't bother to finish" is not the best line. Completion the masters degree is a proof point that you get things done. That is good!
But then again, the degree is not critical. Personally I got a job and worked for a 1.5 years before actually completing my masters degree. But that was back in 1988 and skilled IT professionals were scares to say the least
One more thing - of two persons with similar jobs and background, the one with a masters degree is typically better paid